Hilbert Curves 1.2

Mathemaesthetics, Inc. – Commercial – iOS
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Hilbert Curves is an educational application presented as an interactive electronic document exploring Hilbert's space-filling curve, a renowned mathematical construction. The app delves into the intricacies of mapping points from a line segment to every point within a square through a continuous curve, allowing users to engage in animated infinite zooms and interactive exploration at varying levels of precision.
Going beyond its initial content, this 160-page app uncovers the diverse possibilities stemming from the generalization of the Hilbert Curve construction into a spectrum of intricate space-filling curve designs, patterns, and tiles. From fractal pinwheel curves to impressive half-domino constructions with linear borders and visually striking fuzzy-topped squares, users are guided through these mathematical marvels.
Highlighting an animated Meta-Hilbert construction showcasing the convergence of space-filling curve tile borders to form Hilbert Curves, the app also presents unique half-domino designs resembling indigenous art patterns. In one breathtaking illustration, over 77,000 potential space-filling curve half-domino constructions are displayed, each based on exhaustive enumeration of self-negative "tendril" motifs.
Catering to high-school and college students, math enthusiasts, and professionals intrigued by two-dimensional design patterns, space-filling curves, and fractals, this comprehensive app offers over 130 illustrations within the digital publication "Outside-In and Inside-Gone". Authored by Douglas McKenna, a distinguished mathematical artist and fractal pioneer with a background in space-filling curve research, the content provides unparalleled insight into this intricate field.
Distinctively, the app eschews conventional vectors or PDF files for resolution-independent visuals, opting instead for high-quality typesetting at runtime akin to TeX standards. Through independently zoomable images integrated into the text, users can interact with parameterized illustrations and animations to better comprehend complex mathematical concepts. By dynamically constructing detailed visuals with millions of connected lines that can be extensively explored, this app offers an immersive learning experience tailored to the curious mind.
Representing a decade of meticulous research, writing, and software development efforts, Hilbert Curves emerges as an indispensable visual compendium meticulously crafted to convey the intricacies of this computer-centric subject accurately.

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